Given $ m \angle AOB = 6x + 28$, $ m \angle BOC = 2x + 33$, and $ m \angle AOC = 141$, find $m\angle BOC$. $O$ $A$ $C$ $B$
From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {6x + 28} + {2x + 33} = {141}$ Combine like terms: $ 8x + 61 = 141$ Subtract $61$ from both sides: $ 8x = 80$ Divide both sides by $8$ to find $x$ $ x = 10$ Substitute $10$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 2({10}) + 33$ Simplify: $ {m\angle BOC = 20 + 33}$ So ${m\angle BOC = 53}$.